Eccentric Impact Learning Goal: To be able to use the relationship between the v

Question

Eccentric Impact Learning Goal: To be able to use the relationship between the velocities of two colliding objects and the coefficient of restitution to describe a collision. Eccentric impact occurs when the line connecting the mass centers of two bodies does not coincide with the line of impact. In a collision between two bodies A and B, assuming that the initial velocities (va)1 and (vb)1 along the line of impact are known, there are two unknowns: the final velocities (va)2 and (vb)2. Because there are two unknowns, there must be two equations. The first equation involves theconservation of angular and linear momentum of the bodies. The second equation is the coefficient of restitution,

Itot=

Explanation / Answer

This problem is pretty simple when you break it down into two separate shapes, the slender rod and then the thin circular metal disk. In order to get I_tot we are going to have to add the moment of inertia from the rod and the disk together. First, I_rod = mL^2/3 = (.59kg)(.23m)^2/(3) = 1.04 x 10^-2 kg*m^2 Second, we must find I_rod which is represented as I_d. I_d = I_G + m_d(l+r)^2 I_G = (.25)(mr^2) (due to rotation along the central axis) I_G = (.25)((.82kg)(.0645)^2) = 8.5285*10^-4 kg*m^2 Thus, I_d = (8.5285*10^(-4) kg*m^2) + 0.07112 kg*m^2 = 0.07197 kg*m^2 Now sum the I_rod and I_d to get the I_tot. I_tot = I_rod + I_d = (1.04 x 10^-2 kg*m^2) + (0.07197 kg*m^2) Finally, I_tot = 0.08237 kg*m^2

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